How to enable infinite command history

[Ivan Yosifov]

Hi everyone, 

I got an admittedly basic question but I'm really at my wits' end with
this. 

How do I enable infinite command history ?

One simple suggestion I've seen online is to set HISTSIZE and
HISTFILESIZE to a large number. This is not what I need, I want
genuinely unconstrained history file growth. 

Another idea I've seen is to unset HISTSIZE and HISTFILESIZE. This
doesn't seem to work, the history file is being cropped to the default
of 500 lines.

I'm probably missing something obvious but any help is appreciated. I'm
running Bash 4.1.5 (Debian Squeeze).

Kind regards,
Ivan Yosifov